A variable-gain amplifier or attenuator circuit as shown in FIG. 81 has been heretofore adopted as a volume-adjusting device in audio equipment, TV receivers, communications equipment, etc. to control the volume of an analog audio signal. This circuit comprises resistors R1-Rn+1, an operational amplifier 101, and transistor switches Sw1-Swn controlled by a control circuit 102.
In brief, when a transistor Swi is conducting, no current is fed into the inverting input terminal of the operational amplifier 101 and so a terminal i is placed at the same potential as the inverting input terminal, forming a circuit equivalent to a circuit shown in FIG. 82. At this time, the ON resistance of the switch Swi is independent of the gain.
In FIG. 82, resistances ri and rf are respectively given by EQU ri=R1+R2++Ri EQU rf=Ri+1++Rn+Rn+1
At this time, the gain Gi (dB), i.e., the ratio of the output voltage Vout to the input voltage Vin, is given by ##EQU1## It can be seen from Eq. (1) above that R1-Rn+1 are determined by the desired gain providing either amplification or attenuation that is obtained by selectively closing the switches. This circuit is fabricated often using semiconductor devices to miniaturize the circuit.
If large amplification or large attenuation should be obtained by the gain of the circuit described above, or if the steps of gain are reduced, the ratio of the total resistance to the minimum resistance becomes exorbitantly large. Especially, where the circuit described above is fabricated using semiconductor devices, limitations are frequently imposed on the minimum size of the minimum resistor due to the limited ability to miniaturize resistive elements fabricated and due to limited accuracy achieved. Therefore, as the minimum resistance increases, the area of the whole resistance increases, thus increasing the dimensions of the circuit.
Furthermore, when it is attempted to make the amplification or attenuation as large as possible by the gain of the circuit, the area of the resistor increases. Thus, the limitations placed on the circuit scale have made it impossible to produce large degrees of amplification or attenuation.
The relation of the total resistance to the minimum resistance of the prior art circuit shown in FIG. 81 is next described about the case where the circuit is used for amplification and about the case where the circuit is used for attenuation.
It is first assumed that the circuit shown in FIG. 81 is used as an amplifier circuit having a variable gain. A desired gain providing amplification is derived by selectively closing the switches. Which of the resistors R1-Rn+1 gives the minimum resistance varies, depending on the number of the switches and on the desired gain. For example, where the gain is changed in negative equal steps a (dB) as is often used, R1 or R2 often becomes the minimum resistance. Under this condition, the above-described relation is expressed as described below.
It is now assumed that when the switches S1 and S2 are closed, voltage gains of G1 and G2 are respectively produced (G2=G1+a). Thus, these gains can be respectively expressed as follows. ##EQU2## Note that G1 is the maximum gain of this circuit. When R1 is the minimum resistance, if the total resistance Rall is expressed in terms of the minimum resistance R1, we have ##EQU3## Notice that R1 is the minimum resistance where the following relation holds: ##EQU4## When R2 is the minimum resistance, if the total resistance Rall is expressed in terms of the minimum resistance R2, the total resistance is given by ##EQU5## If the relationship ##EQU6## holds, R2 gives the minimum resistance.
For example, where G1=50 dB and G2=40 dB (gain step=-10 dB), Eq. (5) holds and, therefore, R1 becomes the minimum resistance. Eq. (4) leads to Rall=317.2.times.R1. Consequently, the total resistance must be 317.2 times as large as the minimum resistance.
Where G1=60 dB and G2=59 dB (gain step=-1 dB), Eq. (7) holds and, therefore, R2 becomes the minimum resistance. Eq. (6) leads to Rall=8212.9.times.R2. Consequently, the total resistance must be 8212.9 times as large as the minimum resistance. In this way, the ratio of the total resistance to the minimum resistance is very large.
Generally, however, when an amplifier circuit is designed, allowances are given to the ideal gain providing amplification. Therefore, the values of Rall derived from Eqs. (4) and (6) involve errors.
An example that the circuit shown in FIG. 81 is used as a variable-gain circuit providing attenuation is next described. Again, which of the resistors R1-Rn+1 gives the minimum resistance varies, depending on the number of the switches and on the desired attenuation produced by selectively closing the switches. For example, where the gain is varied in negative equal steps a (dB) as is often used, Rn or Rn+1 often becomes the minimum resistance. This situation is next described.
It is now assumed that when the switches SWn-1 and SWn are closed, voltage gains of Gn-1 and Gn are respectively produced (Gn=Gn-1+a). Thus, these gains can be respectively expressed as follows. ##EQU7## where Gn is the maximum attenuation provided by the gain of this circuit. When Rn+1 is the minimum resistance, expressing the total resistance Rall in terms of the minimum resistance Rn+1 gives rise to ##EQU8## Note that Rn+1 gives the minimum resistance provided that the following relation holds: ##EQU9## When Rn gives the minimum resistance, expressing the total resistance Rall in terms of Rn results in ##EQU10## If the relationship ##EQU11## holds, Rn gives the minimum resistance.
For example, where Gn-1=-40 dB and Gn=-50 dB (gain step=-10 dB), Eq. (11) holds and, therefore, Rn+1 gives the minimum resistance. Eq. (10) leads to Rall=317.2.times.Rn+1. Consequently, the total resistance must be 317.2 times as large as the minimum resistance.
Where Gn-1=-59 dB and Gn=-60 dB (gain step=-1 dB), Eq. (13) holds and, therefore, Rn gives the minimum resistance. Eq. (12) leads to Rall=8212.9.times.Rn. Consequently, the total resistance must be 8212.9 times as large as the minimum resistance. In this manner, the ratio of the total resistance to the minimum resistance is increased greatly.
Generally, however, when an amplifier circuit is designed, allowances are given to the ideal gain providing amplification. Therefore, the values of Rall derived from Eqs. (10) and (12) involve errors.
In the examples given above, the gain is variable and changes in equal steps. Even where the gain step is not uniform, the ratio of the total resistance to the minimum resistance is very large in the configuration described above.